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Spontaneous disruption of cometary nuclei is one of the least understood, but most important aspects of their nature. Attempts to explain the mysterious phenomenon date back to 1846, when in the middle of January astronomers were surprised to see periodic comet Biela had split into two pieces. In the course of time many similar events were discovered and the breakup rate estimated to be close to one per century per comet. Breakups are often accompanied by massive outbursts of brightness, but it is not even clear if it is the outburst that triggers splitting or the other way around. The fate of split comets is frequently the same: their fragments continue to break up and quickly disappear. For example, the two pieces of comet Biela were recovered during the next return in 1852, but have never been seen again. Instead, intense meteor showers were observed during the comet's next expected returns. In spite of this long history and great importance for the determination of cometary lifetimes, the phenomenon remains unexplained to date, although several hypotheses have been proposed. In particular, it has been suggested that the disruption can be caused by nucleus spin-up powered by outgassing torques, which can drive the nucleus spin rate beyond the limit of rotational stability. I will discuss the progress in testing this hypothesis that has happened in the last decade, and overview possible future studies aimed at solving this longest-standing problem in cometary science.